In some versions of the plot, it could be that Dolohov has escaped from Azkaban and is causing trouble again. Hermione, being the brave and resourceful witch she is, decides to take matters into her own hands. She might team up with some old friends or make new allies in her pursuit. She would use her vast knowledge of spells and potions to outwit Dolohov at every turn.
Perhaps Dolohov has some valuable information that Hermione needs for a research project or to protect the wizarding world further. So she tracks him down. She might face many obstacles along the way, like dark magic traps he has set up.
One possible plot could be that Hermione is on a mission to bring Dolohov to justice for his crimes during the wizarding war. She uses her intelligence and magic skills to follow his trail.
I'm not sure of specific 'hermione tracks down dolohov' fanfiction off the top of my head. You could try searching on major fanfiction platforms like Archive of Our Own. There might be some interesting stories there.
One possible plot could be that Hermione is on a mission to gather information from Rodolphus. Maybe she suspects he has some knowledge about the remaining Death Eaters or some dark magic secrets that could help in the post - war rebuilding of the wizarding world.
In a 'hermione meets dolohov fanfiction', perhaps Dolohov is captured by the Order of the Phoenix. Hermione is assigned to interrogate him. At first, they are hostile towards each other. But as they interact more, they start to understand each other's motives a bit better. Dolohov might even start to have second thoughts about his allegiance to the Dark Lord because of Hermione's strong beliefs.
One possible plot could be that the other characters, like Harry and Ron, immediately start a rescue mission. They might search for clues about where Dolohov has taken Hermione. Maybe they discover that Dolohov is working for a more powerful dark wizard who wants Hermione for her knowledge of magic. Then they have to face various traps and dark spells to reach her.
One possible plot could be that in an alternate universe, Dolohov has a change of heart. He somehow crosses paths with Hermione, and they gradually develop an unexpected bond. Eventually, they have a child, and the story could revolve around how they protect their family from the prejudices of both their former worlds.
One possible plot for this fanfiction is that Hermione wants revenge on the Death Eaters who have caused harm to her friends and the wizarding world in general. Dolohov, having once been a Death Eater himself, could provide crucial information about their hideouts, plans, and weaknesses. This would give Hermione an edge in her quest for revenge. He could also use his combat skills, which are no doubt formidable, to protect Hermione during her confrontations with the bad guys.
One possible plot twist could be that Hermione uses her intelligence to outwit Dolohov even while kidnapped. Maybe she manages to leave hidden clues for her friends to find her. Another could be that Dolohov has an ulterior motive other than harming her, like using her as a bargaining chip in the wizarding war. Or perhaps Hermione discovers a hidden power within herself during the time of her captivity that helps her escape.
One difficulty could be that it's a relatively niche plot. Not all fanfiction writers might be interested in exploring this particular scenario of Hermione tracking down Rabastan, so there may be fewer works available. Another issue is that if the fanfiction is not tagged correctly on the platforms, it can be really hard to find using the search function.
I'm not sure of specific 'Hermione tracks down Rodolphus' fanfictions off the top of my head. You could try searching on fanfiction - specific websites like Archive of Our Own or FanFiction.net. Just type in the keywords 'Hermione tracks down Rodolphus' in their search bars, and you might find some interesting stories.
It could also be that Dolohov's desire for Hermione causes a rift among the Death Eaters. Some might see it as a distraction or a sign of weakness. This internal conflict within the Death Eaters could then be exploited by Hermione and her allies to their advantage in the fight against the dark side.